Scala analysis: 541_M49
Miscellaneous tetrachord 68/67 * 67/56 * 56/51
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 68/67 25.648381 2: 17/14 336.129503 supraminor third 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 56/51 161.9155 1: 68/67 25.6484 2: 67/56 310.4811 3: 56/51 161.9155
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 68/67 25.648 cents 1: 1 56/51 161.915 cents 1: 1 67/56 310.481 cents 2: 1 224/201 187.564 cents 2: 1 17/14 336.130 cents supraminor third 2: 1 67/51 472.397 cents Highest number of different intervals for one interval class: 3 Average number of different intervals per interval class: 3.00000 = 3
SHOW/LINE/CENTS INTERVALS
1 2 3 0.0 : 25.6 336.1 498.0 25.6 : 310.5 472.4 498.0 336.1: 161.9 187.6 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 25.6484 .. 310.4811 cents 4489/3808, 284.8327 cents 68/67, 25.6484 cents 2: 187.5639 .. 472.3966 cents 4489/3808, 284.8327 cents 12544/13467,-122.9172 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 68/67, 25.6484 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 67/56, 310.4811 cents Average / Smallest step : 6.472728 Largest / Average step : 1.870199 Largest / Smallest step : 12.105291 Median interval of one step : 56/51, 161.9155 cents, amount: 1 Least squares average step : 156.57446 cents, oct.: 469.72337 cents Scale is not proper Scale has trivalence property Scale is a mode of a 932-tone equal temperament with octave 4/3 degrees: 48 629 932 Least number of segments generator : 467 of 249.557 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 581 of 310.477 cents and inv. generated superset size: 33 = 30 more = 1100.000% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABC Step pattern size order : SLM Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 25.64838 cents Scale diversity : 0.625179 Lumma stability : 0.102996 Lumma impropriety factor : 0.246799 Rothenberg efficiency : 0.666667 redundancy: 0.333333 Efficiency x scale size : 2.000000 Number of different interval sizes : 6 = 3.00000 / class Number of one step interval sizes : 3 Highest interval variety : 3 Mean interval variety : 3.00000 = 3 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 68/67, 25.6484 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% -- Rational properties -- Prime limit : 67 Odd number limit : 201 (O: 67 U: 201) Highest odd numerator or denominator: 67 Scale harmonicity : 0.021706 Fundamental : 1/2814, -11.4584 octaves, 0.0930 Hz. Guide tone : 68, 6.0875 octaves, 17790.538 Hz. Exponens Consonantiae : 1.913520E+05, 17.54587 octaves Euler's gradus suavitatis : 94 Sum of Mann's harmonic distance : 86.5, average 28.83333 Mersenne's string divisions : 29295 Sum of van Prooijen's expressibility: 3.53364, average 1.17788 Sum of Tenney's harmonic distance : 7.11434, average 2.37145 Vogel's harmonic complexity : 64.66667 Wille's k value : 1708 Wilson's harmonic complexity : 94 Rectangular lattice diameter : 4 Triangular lattice diameter : 2 Lattice compactness : 14.24478, average 2.37413 Lattice compactness (without 2's) : 7.56048, average 1.26008 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: -1 .. 2 1.00000 5 3: -1 .. 0 -0.33333 1 1 7: -1 .. 0 -0.33333 1 17: 0 .. 1 0.66667 2 1 67: -1 .. 0 -0.33333 1 1 Average exponent except 2's :-1 / 3 =-0.33333 Average absolute exponent except 2's: 5 / 3 = 1.66667 Scale is weakly epimorphic with val: <6 10 18 27 44| Scale is weakly epimorphic with val: <6 10 19 28 45| Scale is weakly epimorphic with val: <6 10 20 29 43| Scale is weakly epimorphic with val: <6 10 21 30 44| Scale is weakly epimorphic with val: <6 10 22 31 45| Scale is weakly epimorphic with val: <6 11 18 27 43| Scale is weakly epimorphic with val: <6 11 19 28 44| Scale is weakly epimorphic with val: <6 11 20 29 45| Scale is weakly epimorphic with val: <6 11 21 30 43| Scale is weakly epimorphic with val: <6 11 22 31 44| Scale is weakly epimorphic with val: <7 10 18 28 43| Scale is weakly epimorphic with val: <7 10 18 33 44| Scale is weakly epimorphic with val: <7 10 19 29 44| Scale is weakly epimorphic with val: <7 10 20 30 45| Scale is weakly epimorphic with val: <7 10 20 32 43| Scale is weakly epimorphic with val: <7 10 21 31 43| Scale is weakly epimorphic with val: <7 10 21 33 44| Scale is weakly epimorphic with val: <7 10 22 32 44| Scale is weakly epimorphic with val: <7 11 18 27 43| Scale is weakly epimorphic with val: <7 11 18 29 44| Scale is weakly epimorphic with val: <7 11 18 30 43| Scale is weakly epimorphic with val: <7 11 18 32 44| Scale is weakly epimorphic with val: <7 11 18 33 43| Scale is weakly epimorphic with val: <7 11 19 27 45| Scale is weakly epimorphic with val: <7 11 19 28 44| Scale is weakly epimorphic with val: <7 11 19 30 45| Scale is weakly epimorphic with val: <7 11 19 31 44| Scale is weakly epimorphic with val: <7 11 19 33 45| Scale is weakly epimorphic with val: <7 11 20 28 43| Scale is weakly epimorphic with val: <7 11 20 29 45| Scale is weakly epimorphic with val: <7 11 20 31 43| Scale is weakly epimorphic with val: <7 11 20 32 45| Scale is weakly epimorphic with val: <7 11 21 27 43| Scale is weakly epimorphic with val: <7 11 21 29 44| Scale is JI-epimorphic with val: <7 11 21 30 43| Scale is weakly epimorphic with val: <7 11 21 32 44| Scale is weakly epimorphic with val: <7 11 21 33 43| Scale is weakly epimorphic with val: <7 11 22 27 45| Scale is weakly epimorphic with val: <7 11 22 28 44| Scale is weakly epimorphic with val: <7 11 22 30 45| Scale is JI-epimorphic with val: <7 11 22 31 44| Scale is weakly epimorphic with val: <7 11 22 33 45| Scale is weakly epimorphic with val: <7 12 18 28 44| Scale is weakly epimorphic with val: <7 12 18 32 43| Scale is weakly epimorphic with val: <7 12 19 29 45| Scale is weakly epimorphic with val: <7 12 19 33 44| Scale is weakly epimorphic with val: <7 12 20 30 43| Scale is weakly epimorphic with val: <7 12 21 31 44| Scale is weakly epimorphic with val: <7 12 21 32 43| Scale is weakly epimorphic with val: <7 12 22 32 45| Scale is weakly epimorphic with val: <7 12 22 33 44| Scale is weakly epimorphic with val: <8 11 18 29 44| Scale is weakly epimorphic with val: <8 11 18 30 43| Scale is weakly epimorphic with val: <8 11 19 30 45| Scale is weakly epimorphic with val: <8 11 19 31 44| Scale is weakly epimorphic with val: <8 11 20 31 43| Scale is weakly epimorphic with val: <8 11 20 32 45| Scale is weakly epimorphic with val: <8 11 21 30 43| Scale is weakly epimorphic with val: <8 11 21 32 44| Scale is weakly epimorphic with val: <8 11 22 31 44| Scale is weakly epimorphic with val: <8 11 22 33 45| Scale is weakly epimorphic with val: <8 12 18 29 43| Scale is weakly epimorphic with val: <8 12 18 31 44| Scale is weakly epimorphic with val: <8 12 19 30 44| Scale is weakly epimorphic with val: <8 12 19 32 45| Scale is weakly epimorphic with val: <8 12 20 30 43| Scale is weakly epimorphic with val: <8 12 20 31 45| Scale is weakly epimorphic with val: <8 12 21 31 44| Scale is weakly epimorphic with val: <8 12 21 32 43| Scale is weakly epimorphic with val: <8 12 22 32 45| Scale is weakly epimorphic with val: <8 12 22 33 44|
FIT/MODE
3: 0 2 1 N G T3 SD: 14.9961 c. M: 25.6484 c. 12: 1 7 4 N T3 SD: 9.4551 c. M:-15.8554 c. 13: 1 8 4 N T3 SD: 8.8606 c. M:-12.6628 c. 15: 1 9 5 N T3 SD: 4.9625 c. M:-7.5546 c. 16: 1 10 5 N T3 SD: 4.8103 c. M:-6.2764 c. 18: 1 11 6 N T3 SD: 2.6388 c. M: 4.0995 c. 19: 1 12 6 N T3 SD: 2.6976 c. M:-4.6381 c. 21: 1 13 7 N T3 SD: 2.6165 c. M: 4.0995 c. 22: 1 14 7 N T3 SD: 2.6419 c. M:-3.4466 c. 34: 2 21 11 N T3 SD: 2.1544 c. M:-3.6484 c. 37: 2 23 12 N T3 SD: 0.7682 c. M:-1.2730 c. 40: 2 25 13 N T3 SD: 0.4318 c. M: 0.7461 c. 77: 4 48 25 N T3 SD: 0.1783 c. M:-0.2241 c. 117: 6 73 38 N T3 SD: 0.1100 c. M:-0.1573 c. 194: 10 121 63 N T3 SD: 0.1044 c. M:-0.1792 c. 252: 13 157 82 N T3 SD: 0.0885 c. M: 0.1468 c. 292: 15 182 95 N T3 SD: 0.0783 c. M: 0.1197 c. 329: 17 205 107 N T3 SD: 0.0617 c. M:-0.0865 c. 369: 19 230 120 N T3 SD: 0.0292 c. M: 0.0504 c. 446: 23 278 145 N T3 SD: 0.0207 c. M:-0.0356 c. 486: 25 303 158 N T3 SD: 0.0166 c. M: 0.0288 c. 563: 29 351 183 N T3 SD: 0.0169 c. M:-0.0288 c. 815: 42 508 265 N T3 SD: 0.0179 c. M: 0.0255 c. 855: 44 533 278 N T3 SD: 0.0164 c. M: 0.0219 c. 932: 48 581 303 N T3 SD: 0.0019 c. M: 0.0026 c.
FIT/HARMONIC
1 x x 2 S SD: 701.9550 cents 2 x x 3 S SD: 203.9100 cents 3 x x 4 S SD: 0.0000 cents 4 x 5 x S SD: 50.1842 cents 5 x 6:7 S SD: 43.4582 cents 6 x 7:8 S SD: 34.6293 cents 7 x x 9 SD: 62.9609 cents 8 x 10:11 S SD: 36.5939 cents 9 x 11:12 SD: 5.6392 cents 42:43:51:56 SD: 5.0295 cents 47:48:57:63 SD: 4.7807 cents 48:49:58:64 SD: 4.3887 cents 51:52:62:68 SD: 2.7383 cents 57:58:69:76 SD: 2.3266 cents 60:61:73:80 SD: 1.5021 cents 66:67:80:88 SD: 1.0376 cents 75:76:91:100 SD: 1.0128 cents 126:128:153:168 SD: 0.5386 cents 135:137:164:180 SD: 0.2591 cents 201:204:244:268 SD: 0.1689 cents 336:341:408:448 SD: 0.0253 cents